Bibliographic record
Abstract
Let G:=(V,E) be a simple graph; for I⊆V we denote by l(I) the number of components of G[I], the subgraph of G induced by I. For V1,…,Vn subsets of V, we define a function β(V1,…,Vn) which is expressed in terms of l(⋃ni=1Vi) and l(Vi∪Vj) for i≤j. If V1,…,Vn are pairwise disjoint independent subsets of V, the number β(V1,…,Vn) can be computed in terms of the cyclomatic numbers of G[⋃ni=1Vi] and G[Vi∪Vj] for i≠j. In the general case, we prove that β(V1,…,Vn)≥0 and characterize when β(V1,…,Vn)=0. This special case yields a formula expressing the length of members of an interval algebra \cite{s} as well as extensions to pseudo-tree algebras. Other examples are given.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".